Fibre-as-phase-object approximation in light scattering experiments

Abstract

Abstrac t.The use of an optical ® bre scattering pattern for measurements of its refractive-index pro® le and diameter through the ® bre-as-phase-object method is discussed. The exact solution from electromagnetic theory and the phase-object approximation are compared. A great discrepancy between the exact solution and the ® bre-as-phase-object approximation used in recently published papers is demonstrated and is critically analysed.Light di raction from an optical ® bre has been used for many years tomeasure the ® bre refractive index pro® le. Di erent methods were developed to recover ® bre parameters from the di raction pattern [1± 5]. Presby [1] has shown that the diameter of an unclad ® bre can be measured by observing the backscattered light. Watkins [2] has proposed a method in which the pro® le of a ® bre with uniform core was calculated from its scattering pattern. This method was modi® ed for an arbitrary pro® le by Okoshi and Hotate [3]. The drawback of this method is that a large number of data points was required. Later, Brinkmeyer [4] proposed to consider a® bre, which was immersed intoan index-matching oil, as aphase object. In this case the core± cladding refractive-index di erence is very small d n ! 1 and the amplitude distribution of aplane optical wave can be considered tobe constant inside the ® bre; this approach simpli® es the scattering pattern analysis. Recently, a new method has been proposed in [6] in order to determine ® bre parameters. As the author of that paper stated, a ® bre was considered as aphase object; in contrast to the paper of Brinkmeyer, refraction inside the ® bre was taken into account, a consideration thatÐ it was arguedÐ permitted one to avoid the need for an indexmatching oil. In this paper we show that the approach proposed in [6]is incorrect, and cannot be used to determine ® bre parameters. We derive the exact solution from electromagnetic theory, which is in good agreement with previously published experimental and theoretical results of other authors [1± 4], but is absolutely di erent from the theory and experimental results published in [6].We consider plane wave di raction from a dielectric cylinder that corresponds to the case of laser beam scattering from a ® bre. Although the term`di raction' is more correct we will use the term`scattering' following the terminology of previous papers [1± 4]. We assume that the electric ® eld of the incident wave is aligned with the ® bre axis in the vertical plane (® gure 1). In [6] the ® bre was considered as a phase object, which introduces just aphase shift. Such assumption means that the ® bre does not change the ampiltude distribution of alaser beam. In